{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "metadata": {}
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "from scipy.interpolate import RectBivariateSpline\n",
    "from pandas import read_csv\n",
    "import matplotlib.pyplot as plt\n",
    "import yaml\n",
    "from scipy.integrate import cumtrapz\n",
    "from ase.units import kB, GPa\n",
    "root = os.getcwd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "metadata": {}
   },
   "outputs": [],
   "source": [
    "#%matplotlib qt5\n",
    "def calc_rs():\n",
    "    with open(\"ti_spring_300.yaml\", \"r\") as f:\n",
    "        y = yaml.safe_load(f)\n",
    "\n",
    "    T0 = y[\"T\"]\n",
    "    G0 = y[\"G\"]\n",
    "    rs = read_csv(\"ti_rs.csv\")\n",
    "    n = int(len(rs) / 2)\n",
    "    forward = rs[:n]\n",
    "    backward = rs[n:][::-1]\n",
    "    backward.reset_index(inplace=True)\n",
    "    l = forward[\"lambda\"]\n",
    "    H1 = forward[\"enthalpy\"]\n",
    "    H2 = backward[\"enthalpy\"]\n",
    "    T = T0/l\n",
    "    w = (cumtrapz(H1,l,initial=0) + cumtrapz(H2,l,initial=0))*0.5\n",
    "    G = (G0 + 1.5*kB*T0*np.log(l) + w)/l\n",
    "    os.chdir(root)\n",
    "    return T, G\n",
    "\n",
    "T, G = calc_rs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "metadata": {}
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(22.097222222222214, 0.5, 'Free energy (eV/atom)')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(T, G, label=\"Reversible Scaling\")\n",
    "plt.scatter([300, 500, 700, 1000], [-4.5948, -4.6383, -4.7035, -4.8295], label=\"Frenkel-Ladd\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Temperature (K)\")\n",
    "plt.ylabel(\"Free energy (eV/atom)\")\n",
    "plt.savefig(\"TI.pdf\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
